Answer:

Let's represent Beryl's current age as "x".

Whitney's current age can be represented as "x - 7".

Next year, Beryl's age will be "x + 1".

And, Whitney's age will be "x - 7 + 1 = x - 6".

According to the problem statement, next year Beryl will be 1 year more than twice as old as Whitney will be:

x + 1 = 2(x - 6) + 1

Expanding the right side of the equation:

x + 1 = 2x - 11

Solving for x:

3x = 12

x = 4

So, Beryl's current age is 4 years and Whitney's current age is 4 - 7 = -3 years.

The system of linear equations can be represented as:

x + 1 = 2(x - 6) + 1 and x = 4

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